WBJEE · Maths · Limits
The value of \(\lim _{x \rightarrow 0} \frac{1}{x}\left[\int_{y}^{a} e^{\sin ^{2} t} d t-\int_{x+y}^{a} e^{\sin ^{2} t} d t\right]\) is equal to
- A \(e^{\sin ^{2} y}\)
- B \(e^{2 \sin y}\)
- C \(e^{\mid \sin y \mid}\)
- D \(e^{\operatorname{cosec}^{2} y}\)
Answer & Solution
Correct Answer
(A) \(e^{\sin ^{2} y}\)
Step-by-step Solution
Detailed explanation
We have \(\lim _{x \rightarrow 0} \frac{1}{x}\left[\int_{y}^{a} e^{\sin ^{2} t} d t-\int_{x+y}^{a} e^{\sin ^{2} t} d t\right]\) \(=\lim _{x \rightarrow 0} \frac{1}{x}\left[\int_{y}^{a} e^{\sin ^{2} t} d t+\int_{a}^{x+y} e^{\sin ^{2} t} d t\right]\)…
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